{
  "abstract": "Nonlinear shear softening in soils and rocks is commonly described using empirical modulus-reduction laws. In this work, we investigate nonlinear softening within the Eringen--Mindlin micromorphic framework by interpreting its additional constitutive parameters in terms of coupling, internal relaxation, and micro-inertia. The micromorphic continuum is viewed as a dynamically enriched effective medium in which the macroscopic deformation interacts with an internal microstructural deformation field. This interaction naturally produces frequency-dependent effective elastic properties and provides a physical connection between macroscopic wave propagation and unresolved microstructural dynamics. We show that nonlinear shear softening can be described by a progressive reduction of the coupling between macroscopic and internal deformation. As this coupling weakens with increasing shear strain, the effective shear modulus decreases. In the low-frequency limit, the resulting constitutive relation takes a hyperbolic form closely related to the classical Hardin--Drnevich law. The model is validated against laboratory measurements of shear-modulus reduction in sand and reproduces the observed nonlinear behavior with only a small number of physically interpretable parameters. The proposed framework provides a new description of nonlinear softening and frequency-dependent behavior without requiring explicit knowledge of the underlying microstructural geometry. Classical empirical modulus-reduction curves emerge as a macroscopic consequence of the interaction between macroscopic and internal deformation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29503",
  "author_total": 1,
  "authors": [
    {
      "name": "Rafael Abreu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfmhktqzzxx9s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29503",
  "fulltext_url": null,
  "id": "dfmhktqzzxx9s",
  "issns": [],
  "landing_url": "https://hal.science/hal-05802211v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.geo-ph"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "openalex",
      "2505|Nonlocal and gradient elasticity in micro/nano structures"
    ]
  ],
  "openalex": "W7214381885",
  "pdf_url": "https://arxiv.org/pdf/2609.29503",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfmhktqzzxx9s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05802211",
      "source": "hal",
      "url": "https://hal.science/hal-05802211v1"
    },
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29503",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29503"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.geo-ph",
      "subfield": "geophysics"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
    }
  ],
  "title": "A micromorphic constitutive framework for (non)linear softening modeling",
  "title_text": "A micromorphic constitutive framework for (non)linear softening modeling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/dfmhktqzzxx9s",
  "venue": "HAL",
  "versions": []
}